In like manner, a true belief cannot be called knowledge when it is deduced by a fallacious process of reasoning, even if the premises from which it is deduced are true. If I know that all Greeks are men and that Socrates was a man, and I infer that Socrates was a Greek, I cannot be said to “know” that Socrates was a Greek, because, although my premises and my conclusion are true, the conclusion does not follow from the premises.
But are we to say that nothing is knowledge except what is validly deduced from true premises? Obviously we cannot say this. Such a definition is at once too wide and too narrow. In the first place, it is too wide, because it is not enough that our premises should be “true,” they must also be “known.” The man who believes that Mr. Balfour was the late Prime Minister may proceed to draw valid deductions from the true premise that the late Prime Minister’s name began with a B, but he cannot be said to “know” the conclusions reached by these deductions. Thus we shall have to amend our definition by saying that knowledge is what is validly deduced from “known” premises. This, however, is a circular definition: it assumes that we already know what is meant by “known premises.” It can, therefore, at best define one sort of knowledge, the sort we call derivative, as opposed to intuitive knowledge. We may say: “ Derivative knowledge is what is validly deduced from premises known intuitively.” In this statement there is no formal defect, but it leaves the definition of “intuitive” knowledge still to seek.
Leaving on one side, for the moment, the question of intuitive knowledge, let us consider the above suggested definition of derivative knowledge. The chief objection to it is that it unduly limits knowledge. It constantly happens that people entertain a true belief, which has grown up in them because of some piece of intuitive knowledge from which it is capable of being validly inferred, but from which it has not, as a matter of fact, been inferred by any logical process.